Question

spiral review

1. solve each equation. write each solution as a fraction and as a decimal.

equation	solution (fraction)	solution (decimal)
$5y = 3$
$0.3z = 0.09$

problems 7–10: each lap around a track is 400 meters. how many meters will someone run in:

1. 2 laps?
2. 5 laps?
3. $x$ laps?
4. if sol ran 7,600 meters, how many laps did they run? explain your thinking.

Explanation:

Problem 6 (2x=3):

Step1: Isolate x
$x = \frac{3}{2}$
Step2: Convert to decimal
$x = 1.5$

Problem 6 (5y=3):

Step1: Isolate y
$y = \frac{3}{5}$
Step2: Convert to decimal
$y = 0.6$

Problem 6 (0.3z=0.09):

Step1: Isolate z
$z = \frac{0.09}{0.3} = \frac{3}{10}$
Step2: Convert to decimal
$z = 0.3$

Problem 7:

Step1: Calculate meters for 2 laps
$2 \times 400 = 800$

Problem 8:

Step1: Calculate meters for 5 laps
$5 \times 400 = 2000$

Problem 9:

Step1: Express meters for x laps
$400 \times x = 400x$

Problem 10:

Step1: Find laps from meters
$\text{Laps} = \frac{7600}{400} = 19$
Step2: Explain
Each lap is 400m, so divide total meters by meters per lap. $7600 \div 400 = 19$.

2x=3:

Step1: Solve for x
$x = \frac{3}{2}$
Step2: Decimal form
$x = 1.5$

5y=3:

Step1: Solve for y
$y = \frac{3}{5}$
Step2: Decimal form
$y = 0.6$

0.3z=0.09:

Step1: Solve for z
$z = \frac{0.09}{0.3} = 0.3 = \frac{3}{10}$

2 laps:

Step1: Meters = laps × 400
$2×400=800$

5 laps:

Step1: Meters = laps ×400
$5×400=2000$

x laps:

Step1: Meters = laps ×400
$400x$

7600 meters:

Step1: Laps = meters ÷400
$7600÷400=19$
Step2: Explain
Each lap is 400m, so divide total meters by 400 to get laps. 7600/400=19.

Answer:

1. $\frac{3}{2}$, 1.5
2. $\frac{3}{5}$, 0.6
3. $\frac{3}{10}$, 0.3
4. 800 meters
5. 2000 meters
6. $400x$ meters
7. 19 laps